Question

S Two astronauts (Fig. P 11.55 ), each having a mass M , are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v . Treating the astronauts as particles, calculate (e) What is the new rotational energy of the system?

Answer 1

The new rotational energy of the system(RE) = $mv^{2}$

How this is calculated?

• Distance of each astronaut from centre of mass(m)=d/2

• Moment of inertia of system

          $I=m(\frac{d}{2} )^{2}+ m(\frac{d}{2} )^{2}\\ I =\frac{md^{2} }{2}$

• Speed of astronauts=v

• So, angular speed,ω =  $\frac{v}{d/2}$

                                         =$\frac{2v}{d}$

• Rotational energy of system= $\frac{1}{2} I \omega^{2}$

                where, ω= angular speed

               $RE=\frac{1}{2} *\frac{md^{2} }{2}*(\frac{2v}{d})^{2} \\RE =mv^{2}$

What is rotational energy?

• Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy.
• Looking at rotational energy separately around an object's axis of rotation, the following dependence on the object's moment of inertia is observed

To know more about rotational energy , refer:

brainly.com/question/13623190

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